Copyright © 2013 Shiqing Wang and Limin Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the recovery of high-dimensional sparse signals via -minimization under mutual incoherence condition, which is shown to be sufficient for sparse signals recovery in the noiseless and noise cases. We study both -minimization under the constraint and the Dantzig selector. Using the two -minimization methods and a technical inequality, some results are obtained. They improve the results of the error bounds in the literature and are extended to the general case of reconstructing an arbitrary signal.